The Dirichlet problem for a class of curvature equations in Minkowski space

Mengru Guo; Heming Jiao

The Dirichlet problem for a class of curvature equations in Minkowski space

Analysis of PDEs 2024-09-06 v1 Differential Geometry

Authors: Mengru Guo , Heming Jiao

Abstract

In this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on establishing the \emph{a priori} $C^2$ estimates.

Keywords

Dirichlet problem curvature equations Minkowski space spacelike hypersurfaces a priori estimates

Cite

@article{arxiv.2409.03308,
  title  = {The Dirichlet problem for a class of curvature equations in Minkowski space},
  author = {Mengru Guo and Heming Jiao},
  journal= {arXiv preprint arXiv:2409.03308},
  year   = {2024}
}